Staff View
On some singular Sturm-Liouville equations and a Hardy type inequality

Descriptive

TitleInfo
Title
On some singular Sturm-Liouville equations and a Hardy type inequality
Name (type = personal)
NamePart (type = family)
Castro
NamePart (type = given)
Hernán
NamePart (type = date)
1981-
DisplayForm
Hernan Castro
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Brezis
NamePart (type = given)
Haim
DisplayForm
Haim Brezis
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Li
NamePart (type = given)
YanYan
DisplayForm
YanYan Li
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Nussbaum
NamePart (type = given)
Roger
DisplayForm
Roger Nussbaum
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Peletier
NamePart (type = given)
Lambertus A
DisplayForm
Lambertus A Peletier
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2012
DateOther (qualifier = exact); (type = degree)
2012-10
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
The main body of this dissertation can be divided into two separate topics. The first topic deals with a Hardy type inequality for functions belonging to the Sobolev space $W^{m,1}_0(Omega)$, where $mgeq 2$ and $Omega$ is a smooth bounded domain in $RR^N$, $Ngeq 1$. We show that for such functions $uin W^{m,1}_0(Omega)$, one has [ orm{partial^kpt{frac{partial^ju(x)}{d(x)^{m-j-k}}}}_{L^1(Omega)}leq Corm{u}_{W^{m,1}(Omega)}, ] where $j,k$ are non-negative integers such that $1 leq k leq m-1$ and $1leq j+kleq m$, and $d(x)$ is a smooth positive function which coincides with $dist(x,domega)$ near $domega$. The second topic deals with the study of the singular Sturm-Liouville operator {$mathcal L_alpha u:=-(x^{2alpha}u')'$,} where $alpha>0$. We develop a linear theory for such operator by introducing suitable weighted Sobolev spaces and prove existence and uniqueness for equations of the form $mathcal L_alpha u+u=fin L^2$ under both homogeneous and non-homogeneous boundary data at the origin. In addition, the spectrum of the operator $mathcal L_alpha$ is fully described. Finally, we prove existence, non-existence and uniqueness results for positive solutions of the non-linear singular Sturm-Liouville equation $mathcal L_alpha u=lambda u+u^p, u(1)=0$, where $alpha>0$, $p>1$ and $lambdainRR$ are parameters.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_4217
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
ix, 186 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = vita)
Includes vita
Note (type = statement of responsibility)
by Hernán Castro
Subject (authority = ETD-LCSH)
Topic
Sturm-Liouville equation--Numerical solutions
Subject (authority = ETD-LCSH)
Topic
Hardy-Littlewood method
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000066647
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3TX3CXN
Genre (authority = ExL-Esploro)
ETD doctoral
Back to the top

Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Castro
GivenName
Hernan
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2012-09-05 13:34:02
AssociatedEntity
Name
Hernan Castro
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Back to the top

Technical

FileSize (UNIT = bytes)
1349120
OperatingSystem (VERSION = 5.1)
windows xp
ContentModel
ETD
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
1351680
Checksum (METHOD = SHA1)
5b09adc282d1659c70fe5b109302f57889851cc2
Back to the top
Version 8.5.5
Rutgers University Libraries - Copyright ©2024